Some people define the Catskills as the four rural counties west of the Hudson River in SE New York, Green, Ulster, Sullivan and Delaware. However the area of SE Ulster county below the Shawangunk ridge is not really part of the geological Catskills and some extend them up into Albany and Schoharie Counties (I-88 on the NW and the Delaware river on the SW). See also geology.

The Catskill Forest Preserve is defined as the 286,000 acres of state land within the Catskill Park.
The Catskill park (green area on the map below) is bounded on the south by Beaver Kill, on the northwest by the east branch of the Delaware River, on the north by route 28 and Route 23.

During the 19th century, the region became a destination for wealthy urbanites seeking vacation retreats from New York City.
The popularity of the Catskills boomed in the 1920s through 1960s as middle class, second generation immigrant families, including Germans, Czechs, Jews, sought a place to vacation near New York City and many resorts were established in the area.
The larger Jewish resorts (such as Kutsher's, Brown's, and Grossinger's) together became known as the "Borscht Belt." A "Who's Who" of mid twentieth century comedians, such as Mel Brooks, Joan Rivers, Don Rickles and Lenny Bruce, got their start by playing the Catskills resorts.

Farther north, throughout the 20th century, more traditional large-scale resorts, country-style inns and lodges enjoyed success as well. In addition, the Catskills have long been the summer home to thousands of kids and adults attending the area's sleep-away camps.

In recent years, a few small-scale resorts have begun to return to the area, catering to outdoor adventurers and winter snow-sport enthusiasts.

Woodstock Music Festival:
In August, 1969, the Catskills were the site of a music and art festival in the town of Bethel, 43 miles southwest of Woodstock, which was the original location planned. Thirty-two of the best-known musicians of the era appeared during a sometimes rainy weekend in front of nearly half a million concertgoers.

The hit 1987 film Dirty Dancing was set in a Catskills resort in the summer of 1963 (though filmed in Virginia and North Carolina.)
Many other films were set there including scenes from Tootsie.

The Shawangunk Ridge, also known as the Shawangunk Mountains or The Gunks, is a ridge of bedrock, extending from the northernmost point of New Jersey toward the Hudson river near Kingston NY. It is technically the southeastern edge of the Catskill Mountains, but sometimes referred to as a separate mountain range. See Geology below.
It is a legendary eastern rock climbing site.

Geology:
The Catskills are part of the 1 billion year old Appalachian Mountains which extend from the Canadian province of Newfoundland and Labrador in the northeast southwestward to Alabama in the U.S.
The Catskills began existence as a river delta 350 million years ago. Streams flowing off the then-mighty Taconic Mountains deposited sediment where the river met a sea (now the Allegheny Plateau. Eventually the Taconics eroded to their present size and the waters dried up, leaving a mostly flat plain.

During this time period, a meteor is believed to have struck the area. Panther Mountain is the remains of its crater.

The Pocono mountains in NE Pennsylvania are part of the same mountain range.